The CMS Collaboration / Physics Letters B 803 (2020) 135285 5
in bin i
,
“sig” includes the contributions from ttbb, tt2b, and ttb,
and
θ
is a vector of nuisance parameters affecting the predicted
yields of the various processes introduced to model the system-
atic
uncertainties described in the next section. The parameters N
i
are used to estimate the multijet background from the combined
fit of the four regions; they are free parameters in the CRs and are
given by Eq. (2)in the SR. The likelihood also features constraint
terms for each of the nuisance parameters considered in the fit.
Different templates are constructed from ttbbevents matching the
fiducial requirements and from events failing these requirements.
For the fiducial ttbb templates, the effect of nuisance parameters
corresponding to theoretical uncertainties is normalized such that
the ttbbcross section in the fiducial phase space is preserved, i.e.
only shape variations within that phase space and their impact
on the reconstruction efficiency are taken into account. No such
requirement is made for the other templates. The uncertainty in
the measured cross section is obtained by profiling the nuisance
parameters. As described in the next section, some uncertainties
are not profiled and are added in quadrature with the uncertainty
obtained from the fit. The fit is repeated for each of the two fidu-
cial
phase-space definitions for ttbbevents described in Section 3,
leading to different in- and out-of-acceptance ttbb templates. The
total ttbbcross section is obtained by dividing the cross section for
the parton-based fiducial phase space by the acceptance, estimated
using powheg+pythia to be (29.4 ± 1.8)%. Uncertainties affecting
this acceptance correction are detailed in the next section.
7. Systematic uncertainties
Several sources of systematic uncertainties affecting the predic-
tions
for the signal and background processes entering the analysis
are considered. These uncertainties may affect the normalization of
the templates entering the fit, or may alter both their shape and
their normalization. The migration of events between the four re-
gions
is taken into account when relevant. Experimental sources
of uncertainties are taken to be fully correlated for all signal and
background distributions estimated using the simulation, while
only a subset of theoretical uncertainties are correlated among the
tt+jets components.
The modelling of the shape of the b tagging discriminator in
the simulation represents an important source of systematic uncer-
tainty.
Several uncertainties in the calibration of the b tagging dis-
criminator
distribution are propagated independently to the shape
and normalization of the 2DCSV templates. These are related to the
uncertainty in the contamination by light- (heavy-) flavour jets in
the control samples used for the measurement of heavy- (light-)
jet
correction factors, as well as to the statistical uncertainty in
these measurements [50]. Since no dedicated measurement is per-
formed
for cjets, the uncertainty in the shape of the b tagging
discriminator distribution for cjets is conservatively taken to be
twice the relative uncertainty considered for bjets. In total, six
different nuisance parameters are introduced to estimate the un-
certainty
arising from b tagging.
We evaluate the effect of the uncertainty in the jet energy
scale (JES) and jet energy resolution (JER) by shifting the jet four-
momenta
using correction factors that depend on jet p
T
and |η|
for the JES, and jet |η| for the JER [49]. The calibration of the JES
is affected by several sources of uncertainty, which are propagated
independently to the measurement. The uncertainty in the JES is
also propagated to the b tagging calibration, and the resulting ef-
fect
on the distribution of the b tagging discriminators is taken to
be correlated with the effect on the jet momenta.
Uncertainties pertaining to the QGL are estimated conserva-
tively
by removing or doubling the scale factors applied to correct
the distribution of the QGL in the simulation [55]. The uncer-
tainty
in the integrated luminosity is evaluated to be 2.5% [25].
Uncertainties in the trigger efficiency are estimated by varying the
trigger scale factors by their uncertainty, as determined from the
efficiency measurements in data and simulation. The uncertainty
in the modelling of pileup is estimated by reweighting simulated
events to yield different distributions of the expected number of
pileup interactions, obtained by varying the total inelastic pp cross
section by 4.6% [58]. We take into account the limited size of the
simulated samples by varying independently the predicted yields
in every bin by their statistical uncertainties.
Theoretical uncertainties in the modelling of the tt+jets pro-
cess
enter this analysis both through the efficiency to reconstruct
and select ttbbevents, and through the contamination from ttcc
and
ttjj backgrounds. The uncertainties in the renormalization and
factorization scales (μ
R
and μ
F
, respectively) are estimated by
varying both scales independently by a factor of two up or down
in the event generation, omitting the two cases where the scales
are varied in opposite directions, and taking the envelope of the
six resulting variations. Likewise, the uncertainties related to the
choice of the scale in the parton shower is evaluated by varying
the scale in the initial-state shower by factors of 0.5 and 2, and
the scale in the final-state shower by factors of
√
2 and 1/
√
2.
Propagation of the uncertainties associated with the PDFs, as well
as with the value of the strong coupling in the PDFs, has been
achieved by reweighting generated events using variations of the
NNPDF 3.0 set [36]. The impact of the choice of the matching
scale h
damp
= 1.58
m
t
between the matrix-element generator and
the parton shower in powheg is evaluated using simulated samples
generated with different choices of h
damp
= m
t
and 2.24
m
t
[38].
We evaluate the uncertainty related to the UE tune by varying the
tune parameters according to their uncertainties. The uncertainty
from the modelling of colour reconnection in the final state is eval-
uated
by considering four alternatives to the pythia default, which
is based on multiple-parton interactions (MPI) with early reso-
nance
decays (ERD) switched off. These alternatives are an MPI-
based
scheme with ERD switched on, a QCD-inspired scheme [59],
and a gluon-move scheme with ERD either off or on [60]. All the
alternative models were tuned to LHC data [61]. It has been ver-
ified
that the selection efficiency obtained from the nominal tt
simulation,
in which additional bjets are generated by the parton
shower, is in agreement within estimated modelling uncertainties
with that obtained using a sample of ttbbevents generated at
NLO in QCD with massive bquarks (4FS) [19]. Since the spec-
trum
of the top quark p
T
is known to be softer in the data than
in the simulation, we evaluate the effect of this mismodelling by
reweighting the generated events to match the top quark p
T
dis-
tribution
measured in data [62]. The latter two uncertainties are
not evaluated using profiled nuisance parameters, but by repeating
the measurement using varied signal and background predictions.
The differences in the measured cross sections are taken as the
corresponding uncertainties and are added in quadrature with the
uncertainty obtained from the profile likelihood. Uncertainties re-
lated
to the μ
R
and μ
F
scales, the parton shower scale, and the
h
damp
choice are taken to be uncorrelated for the ttbb, ttb, tt2b,
ttcc and ttjj templates, while the other modelling uncertainties are
taken to be correlated for all ttevents. In addition to the afore-
mentioned
modelling uncertainties, we assign an uncertainty of
50% to the normalization of the ttccbackground to cover the lack
of precise measurements of this process. The results are stable
when doubling that uncertainty.
Compared to tt+jets and multijet production, the contribution
of other background processes such as ttV, ttH, V+jets, diboson,
and single top quark production is small. We assign uncertainties
to their predicted rates based on the PDF and μ
R
/μ
F
scale uncer-
tainties
in their theoretical cross sections.
Table 1 summarizes the contributions of the various sources
of systematic uncertainties to the total uncertainty in the cross